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Application of the Conditional Nonlinear Optimal Perturbations Method in Sensitivity Analysis of the Lake Eutrophication

Author: ZhangPeiJun
Tutor: WangBo
School: Henan University
Course: Computational Mathematics
Keywords: CNOP Spectral projected gradient Tangent linear model Adjoint model Lake eutrophication
CLC: O342
Type: Master's thesis
Year: 2011
Downloads: 34
Quote: 0
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Abstract


Lake eutrophication problem has become one of the world today between the Government and the public is most concerned about environmental issues . Lake in the process of eutrophication , the formation of an in-house full of complex physical , chemical and biological reactions , nonlinear ecosystem open Numerical experiments equation for the dynamic changes of the shallow lake nutrient concentrations Mu Mu proposed conditions nonlinear optimal perturbation (CNOP) method , respectively, to study the sensitivity of the ecosystem of the initial perturbation and parameter perturbation . the results are as follows : ( 1 ) study the impact of the steady-state transformation of nutrient input rate c of lake ecosystems . when c is less than the bifurcation point c , regardless of the initial finite amplitude perturbation How oligotrophic equilibrium nonlinear stable , suggesting that human short-term activities or the nature of the changes will not make the system steady-state conversion ; when c is greater than the bifurcation point c 2 , nutritious chemical equilibrium is stable , once the lake system developed into a state of eutrophication , it is difficult to restore it to clear state through human effort ; when the the c located c 1 and c 2 < / sub> , the lake ecosystem is fragile equilibrium state and eutrophication of oligotrophic stable equilibrium are linear , but nonlinear unstable , suggesting that certain finite amplitude perturbation to the system of two between the equilibrium conversion under the same constraints , for different c , corresponding CNOP-I of the development is different , this paper presents the initial disturbance is given each nutrient input rate c corresponding critical the the value δ c (2 ) by means of numerical simulation , has been the parameter c in the given constraints , so that the greatest change in the disturbance of the ecosystem development . Numerical results show that the nutrient input rate excellent disturbance to the ecological system to the development of other changes in steady-state conversion maximum . when c is less than the bifurcation point c 2 , the perturbation constraints more than the absolute value of the bifurcation point | c 2 - c |, the original is in the oligotrophic lakes equilibrium ecological system is easy to form the state of eutrophication ; when c is greater than bifurcation point c 1 , in eutrophic the state of the lakes , the absolute value of the if the constraints disturbance exceeds the c 1 - c | c disturbance can make the original eutrophication recovery clear state .

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CLC: > Mathematical sciences and chemical > Mechanics > Solid Mechanics > Structural Mechanics
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